Sažetak:
In this talk we recall the definition and main properties of conformal superalgebras. Then we present the classification of the finite irreducible modules over the conformal superalgebra K'_4 obtained by their correspondence with finite conformal modules over the associated annihilation superalgebra A(K'_4). This is achieved by a complete classification of singular vectors in generalized Verma modules for A(K'_4). We also show that morphisms between generalized Verma modules can be arranged in infinitely many bilateral complexes. This classification is a joint work with F. Caselli.

Then we present a result on the homology of these complexes that provides an explicit realization of all irreducible quotients.